[EM]Ranked-Pairs (wv) can lose a Cond. Winner

[Elisabeth Varin/Stephane Rouillon]

Adam--

I fully agree with your way of seeing things.
It is only about a matter of proportion were we do not see things the same.
I will use samples of what follows.

> But if you shift the percentages
> around a little, or reduce the degree of truncation a bit in the edge
> factions, then it breaks down.  Truncation only works strategically in
> winning votes when there is a lot of truncation (indifference) to start,
> and even then it only works in specific cases with fractured electorates,
> where the Condorcet winner has pretty poor support from other factions.
>
With 3 candidates, I have to agree with you, even if I haven't yet done the
calculus... It seems
easier to build cases against margins than against winning votes. I do not know for
relative
margins...

For more candidates, I do not know. But I think we have a problem of reference.
You seem to be interested into american presidential election, with typically a
small
number of candidates (3 non-negligeable last time). I like it, but an electoral
system
should work well when multiple candidates run for office. Usually I think the more
alternative a voter is offered, the more different debates and positions are
offered
and the healthier the democracy (if this does not paralyse the system by
vote-splitting).
French got 17 official candidates last time. If I remember well, 15 were
non-negligeable
(it means by rallying their vote to the third runner, they could have changed the
outcome
of the election). In such a case, with 17 candidates, please do not tell me that
truncation
from start (sincer preferences) would not be the natural way to vote... (less than
60% of
voters go vote already, and we only ask them to pick one name!)

I admit my sincere Condorcet Winner has a "poor support" (thanks for answering with
a good
example for what I asked Mike) compared to your sincere Condorcet Winner.
But what is more realistic? Identifying and convincing 18% of the voters to tilt
their preferences
from poll predictions as in my case, or 49% in your case. As you said my case is
very unstable,
I bet I would convince nobody. But what about yours? Even if I admit it is very
more probable
than mine, how probable is it? 1% of the cases? We definitively need to compute
this number,
even for the not so simple 3 candidates case with a small number of voters.
Compared to the polls
precision of 9 different ballots (A, B, C, ABC, ACB, BAC, BCA, CAB , CBA) I think
you would still
convince nobody. Finally, with 4 candidates or more, forget polls precision, forget
identifying voters
with the same rankings, forget strategy at all. It has no mathematical relevance.
It is too small cases.

Since sincere preferences seem the most probable input, I think we should consider
an equal probability
of the 9 different ballots. I hope we can create a stealing CW case with few
voters, because only with
4 voters we have 6561 equiprobable simulation cases...

The next thing we will have to do is look at what happens when the number of
candidates or/and voters
inceases. Would the ratio (CW can be stolen cases / voting simulations) increase or
diminish in each case?

> This will be true in a huge range of cases -
> basically, any time the second-place candidate's support for the winner
> allows the winner to beat another edge candidate.  You can fudge the
> numbers in the above example around a large amount and get the same results
> - provided you don't give the George faction an absolute majority of course.
>

To summarize, I believe your "huge range of cases" will be incredibly small
compared to the overall range of possibilities...
And polls will not be sufficient to make it trustable enough, unless they can
garantee less than 5 % errors and their result is your example.
With your ideal example for winning votes a 6% error per kind of ballot could twist
the result against truncaters wishes:

43%: George>Al>Ralph
6%: Al>George>Ralph
18%: Al>Ralph>George
33%: Ralph>Al>George

So in your ideal case, yes you could convince some people. But even then, after
looking at the real numbers, in most of the cases it would not change the
outcome... (George would have won and still does, or Al would have won and still
does) after polls errors corrections.
I do not think preventing unsincere truncation should be the main issue. To me,
optimal fairness of the representation of the wish of the people should.
Unsincere truncation will almost never happen. Sincere truncation will almost
always happen.

Steph.

Adam Tarr a écrit :

> >This appears to be an example that illustrates a more stable outcome is
> >achievable
> >by counting equal ranked options 1/2 vote each.
>
> Matt, we went over this before.  By adding 1/2 of a vote for each side, you
> turn winning votes into margins.  It's not a compromise in-between the two
> at all - it becomes margins exactly.  Adding half-votes in margins does not
> change the outcome at all.  So since Stephane cooked up his example
> specifically to show when winning-votes encourages truncation (and margins
> does not) it's not surprising that adding half-votes "solves" the problem.
>
> The reality, though, is that it's significantly easier to come up with
> examples where truncation is encouraged in margins-based methods.  Here's
> the example Stephane came up with, casted into percentages and given some
> familiar names:
>
> 36% George
> 9% Al>George>Ralph
> 18% Al>Ralph>George
> 18% Ralph>Al>George
> 19% Ralph
>
> Ralph is the Condorcet winner, but truncation by the middle 18%, in winning
> votes, will give the election to Al.  But if you shift the percentages
> around a little, or reduce the degree of truncation a bit in the edge
> factions, then it breaks down.  Truncation only works strategically in
> winning votes when there is a lot of truncation (indifference) to start,
> and even then it only works in specific cases with fractured electorates,
> where the Condorcet winner has pretty poor support from other factions.
>
> Contrast that to this case, which is not hard to come up with at all:
>
> 49%: George>Al>Ralph
> 12%: Al>George>Ralph
> 12%: Al>Ralph>George
> 27%: Ralph>Al>George
>
> Al is the Condorcet winner.  Now, if the George voters truncate in margins,
> they win the election.  This will be true in a huge range of cases -
> basically, any time the second-place candidate's support for the winner
> allows the winner to beat another edge candidate.  You can fudge the
> numbers in the above example around a large amount and get the same results
> - provided you don't give the George faction an absolute majority of course.
>
> Winning votes gives the election to Al, even if George voters truncate.  If
> you add half-votes, then you run into the same problems you have with
> margins -- naturally, since adding half-votes turns winning votes into margins.
>
> -Adam
>
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